Speaker：XIAO Lechao，University of Pennsylvania

Time: 2016-07-09, 10:00-11:00

Place：Room 1418, School of Mathematical Sciences 

Detail：One basic problem in algebra is finding roots for a polynomial. A central topic in modern harmonic analysis is finding (sharp) estimates for various oscillatory integrals. In the 17th century, Newton introduced a method, known as Newton-Puiseux algorithm, for solving a polynomial $f(x,y) = 0$ by a fractional power series, $y = y(x^{\frac 1 m})$. In this talk, we will illustrate how one can upgrade this algorithm to find sharp estimates for some oscillatory integrals.

Organizer: School of Mathematical Sciences